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Evolving a Nelder-Mead Algorithm for Optimization with Genetic Programming.

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Summary
This summary is machine-generated.

Genetic programming evolved a novel direct search optimization algorithm, improving upon the Nelder-Mead method. This simplified, genetically evolved algorithm demonstrates superior performance on test functions.

Keywords:
Derivative-free optimizationDirect search methodsDownhill simplex methodGenetic programmingHyper-heuristicMeta-optimizationNelder–Mead

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Area of Science:

  • Computational Intelligence
  • Numerical Optimization
  • Evolutionary Computation

Background:

  • The Nelder-Mead method is a widely used direct search optimization algorithm.
  • Developing more efficient and robust optimization algorithms is crucial for scientific research.

Purpose of the Study:

  • To evolve a direct search optimization algorithm using genetic programming.
  • To compare the performance of the evolved algorithm against the standard Nelder-Mead method.

Main Methods:

  • Genetic programming was employed to evolve an optimization algorithm.
  • The training involved ten-dimensional quadratic functions with randomized parameters and starting simplices.
  • The evolved algorithm was tested against a standard set of benchmark functions.

Main Results:

  • The genetically evolved algorithm outperformed the original Nelder-Mead method.
  • Redundant components of the evolved algorithm were identified and removed.
  • The simplified algorithm maintained superior performance compared to the Nelder-Mead method.

Conclusions:

  • Genetic programming can effectively evolve superior optimization algorithms.
  • Simplification of evolved algorithms is possible without compromising performance.
  • The evolved, simplified algorithm offers a more efficient alternative to the Nelder-Mead method.